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Wind Turbine - Cp Vs λ



Learn about the coefficient of power and tip speed ratio of a wind turbine.

Experimental Setup

The turbine is setup to operate with the wind from a blower fan. Wind is blown at differnet speeds, as selected by the user. The amrita setup for windturbine experiments is shown in the picture below. The small windturbine on the background is a backup, if the other one fails.

Calculation of Coefficient of power

The coefficient of power of a wind turbine is a measurement of how efficiently the wind turbine converts the energy in the wind into electricity.

Coefficient of power =( Power produced by the wind turbine/Total power available in the wind)

Where total power in wind flowing through an imaginary area A is:
P=1/2*mv2 = ½*(Avp)v2 = ½*Apv3
Where ‘p’ is the density of the air, ‘v’ is the wind speed, ‘Avt’ is the volume of air passing through A. ‘Avρ’ is therefore the mass m passing per unit time. We know ½*pv2 is the kinetic energy of the moving air per unit volume.

Therefore total available power in the air flow is P = ½*Apv3

We know power produced by the turbine is V*I

Coefficient of power = (VI)/(1/2Apv3)

The Betz Limit is the maximal possible Cp=16/27=0.593

A maximum of 59.3% of the available wind power can be converted to mechanical power at ideal conditions, whatever the energy conversion device is.

Real wind generators do not reach this theoretical optimum; however, good systems have power coefficients Cp between 0.4 and 0.5. 

Calculation of Tip Speed Ratio:

The tip speed ratio for wind turbines is the ratio of the transalational speed at the tip of the turbine blade to the actual velocity of the wind.

Tip speed ratio, λ = Tip speed of blade/ wind speed

lambda =frac{omega *r}{v}

where omega is the rotational speed in radians per second, r is the rotor radius in meters and v is the wind speed meters/second.

The given below is an illustration of the  Cp - λ curve for a typical wind turbine.

Cite this Simulator:

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